# Propulsion

Theory
Propulsion equation. This is the equation that links the electrical power, the propulsive force and the ISP.
Pe = F x ISP *9,81 / 2n or Pe = F x Ev /2n
Pe = electric power (Watts)
F = Engine force (Newtons)
ISP = Specific impulse (Seconds)
n = efficiency of electric engine
9,81 conversion factor
Ev = Exhaust velocity (m/s)
Specific impulse.
ISP = Ev / 9,81
ISP = Specific impulse (Seconds)
Ev = Exhaust velocity (m/s)
Fuel consumption
m = F/Ev
m = Fuel consumption (kg/s)
F = Force (Newtons)
Ev = Exhaust velocity (m/s)
Velocity
V = Ev x ln(Mo/Mf)
Ev = Exhaust velocity (m/s)
V = ship final velocity (m/s)
ln = natural logarithm
Mo = Initial mass of the ship (kg)
Mf = Final mass of the ship (kg)
Key performance parameters
Propulsive force (Thrust)
The propulsive force is the force the engines produce to push the ship. This is factor of the available electrical energy, the engine efficiency and the propulsive system ISP and ejection velocity.
For the Enterprise: Available electrical energy = 2,5 GWe
ISP = 5000
Efficiency (n) = 80%
Thrust = 2 500 000 000 W x 2 x 0,8 / (5000*9,81) = 84 000 N = 8 300 kg = 8,3 Tons